Can a relation be a function without being injective?

📌 CONCEPT: A function is a relation where every element of the domain corresponds to exactly one element in the range, but it does not necessarily have to be injective, meaning multiple elements in the domain can map to the same element in the range.

📐 RULE / FORMULA: For a relation to be a function, it must satisfy the condition that every element of the domain is mapped to exactly one element in the range.

💡 WORKED EXAMPLE: Consider the relation R = {(2, 1), (3, 1), (4, 1), (5, 1)} on the set A = {1, 2, 3, 4, 5}. This relation is a function because every element of the domain (2, 3, 4, 5) corresponds to exactly one element in the range (1).

⚠️ COMMON MISTAKE: Students often mistakenly believe that a function must be injective, meaning it must map different elements in the domain to different elements in the range. However, this is not a requirement for a relation to be a function.